ORDERING FRACTIONS WITH DIFFERENT DENOMINATORS

Order each set of fractions from least to greatest : 

Example 1 :

3/4, 5/8, 11/12

Solution :

Least common multiple of (4, 8, 12) = 24.

3/4 = (3 ⋅ 6)/(4 ⋅ 6) = 18/24

5/8 = (5 ⋅ 3)/(8 ⋅ 3) = 15/24

11/12 = (11 ⋅ 2)/(12 ⋅ 2) = 22/24

Compare the numerators of like fractions above and order them from least to greatest. 

15/24, 18/24, 22/24

Substitute the corresponding original fractions. 

5/8, 3/4, 11/12

Example 2 :

3/4, 2/5, 1/8, 7/10

Solution :

Least common multiple of (4, 5, 8, 10) = 40.

3/4 = (3 ⋅ 10)/(4 ⋅ 10) = 30/40

2/5 = (2 ⋅ 8)/(5 ⋅ 8) = 16/40

1/8 = (1 ⋅ 5)/(8 ⋅ 5) = 5/40

7/10 = (7 ⋅ 4)/(10 ⋅ 4) = 28/40

Compare the numerators of like fractions above and order them from least to greatest. 

5/40, 16/40, 28/40, 30/40

Substitute the corresponding original fractions. 

1/8, 2/5, 7/10, 3/4

Example 3 :

11/15, 9/10, 7/12, 17/20

Solution :

Least common multiple of (15, 12, 20) = 60.

11/15 = (11 ⋅ 4)/(15 ⋅ 4) = 44/60

9/10 = (9 ⋅ 6)/(10 ⋅ 6) = 54/60

7/12 = (7 ⋅ 5)/(12 ⋅ 5) = 35/60

17/20 = (17 ⋅ 3)/(20 ⋅ 3) = 51/60

Compare the numerators of like fractions above and order them from least to greatest. 

35/60, 44/60, 51/60, 54/60

Substitute the corresponding original fractions. 

7/12, 11/15, 17/20, 9/10 

Example 4 :

-1/6, -5/12, -8/9, -7/18

Solution :

Least common multiple of (6, 12, 18) = 36.

-1/6 = (-1 ⋅ 6)/(6 ⋅ 6) = -6/36

-5/12 = (-5 ⋅ 3)/(12 ⋅ 3) = -15/36

-8/9 = (-8 ⋅ 4)/(9 ⋅ 4) = -32/36

-7/18 = (-7 ⋅ 2)/(18 ⋅ 2) = -14/36

Compare the numerators of like fractions above and order them from least to greatest. 

-32/36, -15/36, -14/36, -6/36

Substitute the corresponding original fractions. 

-8/9, -5/12, -7/18, -1/6

Order each set of fractions from greatest to  least : 

Example 5 :

3/4, 2/5, 5/8, 1/2

Solution :

Least common multiple of (4, 5, 8, 2) = 40.

3/4 = (3 ⋅ 10)/(4 ⋅ 10) = 30/40

2/5 = (2 ⋅ 8)/(5 ⋅ 8) = 16/40

5/8 = (5 ⋅ 5)/(8 ⋅ 5) = 25/40

1/2 = (1 ⋅ 20)/(2 ⋅ 20) = 20/40

Compare the numerators of like fractions above and order them from greatest to least. 

30/40, 25/40, 20/40, 16/40

Substitute the corresponding original fractions. 

3/4, 5/8, 1/2, 2/5

Example 6 :

1/6, 1/3, 3/14, 2/7

Solution :

Least common multiple of (6, 3, 14, 7) = 42.

1/6 = (1 ⋅ 7)/(6 ⋅ 7) = 7/42

1/3 = (1 ⋅ 14)/(3 ⋅ 14) = 14/42

3/14 = (3 ⋅ 3)/(14 ⋅ 3) = 9/42

2/7 = (2 ⋅ 6)/(7 ⋅ 6) = 12/42

Compare the numerators of like fractions above and order them from greatest to least. 

14/42, 12/42, 9/42, 7/42

Substitute the corresponding original fractions. 

1/3, 2/7, 3/14, 1/6

Example 7 :

5/6, 11/5, 9/16, 3/4

Solution :

Least common multiple of (6, 5, 16, 4) = 240.

5/6 = (5 ⋅ 40)/(6 ⋅ 40) = 200/240 

11/5 = (11 ⋅ 48)/(5 ⋅ 48) = 528/240

9/16 = (9 ⋅ 15)/(6 ⋅ 16) = 135/240

3/4 = (3 ⋅ 60)/(4 ⋅ 60) = 180/240

Compare the numerators of like fractions above and order them from greatest to least. 

528/240, 200/240, 180/240, 135/240

Substitute the corresponding original fractions. 

11/5, 5/6, 3/4, 9/16

Example 8 :

-5/6, -1/3, -7/12, -3/4

Solution :

Least common multiple of (6, 3, 12, 4) = 12.

-5/6 = (-5 ⋅ 2)/(6 ⋅ 2) = -10/12 

-1/3 = (-1 ⋅ 4)/(3 ⋅ 4) = -4/12

-7/12 = (-7 ⋅ 1)/(12 ⋅ 1) = -7/12

-3/4 = (-3 ⋅ 3)/(4 ⋅ 3) = -9/12

Compare the numerators of like fractions above and order them from greatest to least. 

-4/12, -7/12, -9/12, -10/12

Substitute the corresponding original fractions. 

-1/3, -7/12, -3/4, -5/6

Example 9 :

Jenny had a pizza that was divided into 8 equal slices. She ate 3 of them. Danny has a pizza that is the same size, but his is divided into 4 equal slices. He ate 3 slices of his pizza. Who ate more pizza?

Solution :

Quantity of Pizza Jenny ate = 3/8

Quantity of pizza Danny ate = 3/4

To compare who ate more, we have to make the denominators same and compare the numerators.

LCM (4, 8) = 8

3/4 = (3/4) x (2/2)

= 6/8

Now comparing the fractions 3/8 and 6/8, 6/8 is greater. Then Danny ate more pizza.

Example 10 :

Kim made two pies that were exactly the same size. The first pie was a cherry pie, which she cut into 6 equal slices. The second was a pumpkin pie, which she cut into 12 equal pieces. Kim takes her pies to a party. People eat 3 slices of cherry pie and 6 slices of pumpkin pie. Did people eat more cherry pie or pumpkin pie?

Solution :

Equal number of slices of cherry pie = 6

Number of cherry pie she ate = 3

Fraction part of cherry pie = 3/6

Equal number of slices of pumpkin pie = 12

Number of pumpkin pie she ate = 6

Fraction part of pumpkin pie = 6/12

LCM(6, 12) = 12

3/6 = 3/6 x (2/2)

= 6/12

So, they ate same quantity of pies.

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